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A321568
Least prime p such that p plus the sum of its digits is the n-th prime after p.
2
11, 19, 37, 59, 97, 55787, 26699, 663959, 6974477, 86966771, 1095975857, 4649574977, 349685387573, 988839709939, 86396869388567
OFFSET
1,1
COMMENTS
The other way round is not feasible because p minus the sum of its digits is never a prime but a multiple of 9.
LINKS
Carlos Rivera, Puzzle 935. pi+SOD(pi)=p(i+n), The Prime Puzzles and Problems Connection.
EXAMPLE
a(1) = 11 because 11 + 1 + 1 = 13 that is the first prime after 11.
a(2) = 19 because 19 + 1 + 9 = 29 that is the second prime after 19.
MAPLE
P:=proc(q) local a, b, c, d, n, x; x:=0; d:=[]; for n from 1 to q do
x:=nextprime(x); a:=x+convert(convert(x, base, 10), `+`);
if isprime(a) then c:=0; b:=x; while b<a do b:=nextprime(b); c:=c+1; od;
if numboccur(c, d)=0 then d:=[op(d), c]; lprint(c, x, a); fi; fi;
od; end: P(10^13); # Terms not in order.
MATHEMATICA
Array[Block[{p = 2}, While[p + Total@ IntegerDigits@ p != NextPrime[p, #], p = NextPrime@ p]; p] &, 8] (* Michael De Vlieger, Dec 17 2018 *)
CROSSREFS
KEYWORD
base,nonn,more
AUTHOR
Paolo P. Lava, Dec 17 2018
EXTENSIONS
a(12)-a(15) from Giovanni Resta, Dec 17 2018
STATUS
approved